Localized surface modes

The harmonic-oscillator and elastic-continuum models can be used to explain the presence of surface phonons (Rayleigh waves and localized surface modes of vibration) and the larger mean-square displacement of surface atoms compared to that of atoms in the bulk. 

The birefringence as well as the ffee-carrier dichroism exhibited by por-Si in IR spectral region originates from the anisotropy of nanocrystals and voids comprising the material. The local surface mode dichroism is highly sensitive to the microrelief of the nanocrystal surface. The surface reconstruction of por-Si upon selective thermodesorption of hydrogen is demonstrated. This process results in a considerable increase in the concentration of surface H-terminated dimers. 

From each bulk band, at least one surface mode originates, as shown in Figure 9.46. According to Rayleigh s theorem [82], the number of localized surface modes from each bulk band is given by the number of degrees of freedom, which are affected by the surface perturbation. For an ideal bulk-terminated surface, as in the model calculation of Figure 9.46, no more than one surface phonon mode is expected for each bulk band. 

Uwada T, Asahi T, Masuhara H, Ibano D, Fujishiro M, Tominaga T (2007) Multiple resonance modes in localized surface plasmon of single hexagonal/triangular gold nanoplates. Chem Lett 36(2) 318-319... 

Vp(fO is peaked at the surface. Many collective oscillations manifest themselves as predominantly surface modes. As a result, already one separable term generating by (74) usually delivers a quite good description of collective excitations like plasmons in atomic clusters and giant resonances in atomic nuclei. The detailed distributions depends on a subtle interplay of surface and volume vibrations. This can be resolved by taking into account the nuclear interior. For this aim, the radial parts with larger powers and spherical Bessel functions can be used, much similar as in the local RPA [24]. This results in the shift of the maxima of the operators (If), (12) and (65) to the interior. Exploring different conceivable combinations, one may found a most efficient set of the initial operators. 

The greater the order of the normal mode, the more the field is localized near the surface of the sphere, hence the designation surface modes. The lowest-order mode (n = 1) is uniform throughout the sphere, and this mode is sometimes called the mode of uniform polarization. 

While the electronic structure calculations addressed in the preceding Section could in principle be used to construct the potential surfaces that are a prerequisite for dynamical calculations, such a procedure is in practice out of reach for large, extended systems like polymer junctions. At most, semiempirical calculations can be carried out as a function of selected relevant coordinates, see, e.g., the recent analysis of Ref. [44]. To proceed, we therefore resort to a different strategy, by constructing a suitably parametrized electron-phonon Hamiltonian model. This electron-phonon Hamiltonian underlies the two- and three-state diabatic models that are employed below (Secs. 4 and 5). The key ingredients are a lattice model formulated in the basis of localized Wannier functions and localized phonon modes (Sec. 3.1) and the construction of an associated diabatic Hamiltonian in a normal-mode representation (Sec. 3.2) [61]. 

Degiron A, Ebbesen TW (2005) The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures. J Opt A Pure Appl Opt 7 S90-S96... 

The surface Fuchs-Kliewer modes, like the Rayleigh modes, should be regarded as macroscopic vibrations, and may be predicted from the bulk elastic or dielectric properties of the solid with the imposition of a surface boundary condition. Their projection deep into the bulk makes them insensitive to changes in local surface structure, or the adsorption of molecules at the surface. True localised surface modes are those which depend on details of the lattice dynamics of near surface ions which may be modified by surface reconstruction, relaxation or adsorbate bonding at the surface. Relatively little has been reported on the measurement of such phonon modes, although they have been the subject of lattice dynamical calculations [61-67],... 

Lu Y, Liu GJ, Lee LP (2008) High density self assembled nanoparticle film with temperature-controllable interparticle spacing for deep sub-wavelength nanolithography using localized surface plasmon modes on planar silver nanoparticle tunable grating. Microelectron Eng... 

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